You need to convert the DBX files using third party programs. I have a blog post here http://thunderbirdtweaks.blogspot.com.au/2011/07/outlook-express.html with links to undbx. It is free, but a command line tool. If you want a GUI, this is one of the better on offer in my experience. http://www.maildev.com/buy/ but it will cost you.

Thanks for the possible solution.

However, as it turns out, I eventually thought of another way which I implemented. I installed XP in a virtual machine using VMWare on my Windows 8 machine. (I wanted to do that anyway.) Then I copied the relevant mail files off of the old XP hard drive and over to the newly installed XP, where I could then import them into a working Outlook Express. (At this point, I also did a fairly thorough cleaning of the archived mail.) Then I installed Thunderbird and in the XP guest and did the mail-files-import in the working XP context. I could then copy the resulting Thunderbird profile to the host Windows 8 machine to work with Thunderbird there.

You surely can import Outlook Express mails on Thunderbird but have to use the exterior tool like (removed) which is relevant app. It properly converts .dbx files in .eml file and then simply allows to access files on Thunderbird (on windows 8.1). I recommend you to try it-

Moderator removed link promoting paid software. Please see the forum spam section of Rules & Guidelines, thanks.

The DBX conversion program suggested by ariaevans0 cost $69, so it was appropriate that the moderator removed the link. Oddly, in addition to the free command line tool which Matt suggested, he also suggested a non-free (but more reasonable at $29) GUI solution, the link for which was not removed - I suppose because Matt's suggestion was almost certainly not spam.

Meanwhile, as I already stated, I had solved my problem using a newly installed XP.